Generating entangled Schrödinger cat states using a number state and a beam splitter

Abstract

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrödinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.

Destructive Controlled-Phase Gate using Linear Optics

“…This is acceptable in a number of applications where the control qubit would have been destroyed in any event, such as in a postselection process. Potential applications of this kind include the generation of Schrodinger cat states 2 , nonlocal interference experiments that violate Bell's inequality 4 , and the construction of cluster states using fusion gates 11 . The control qubit can always be preserved if necessary by using a quantum encoder circuit 10 before the controlled-phase gate, but that would require two ancilla photons and there would be no benefit as compared to the original KLM controlled-phase gate.…”

“…The KLM gate preserves the control qubit whereas it is destroyed in the controlled-phase gate of Figure 4. As noted previously, a destructive controlled-phase gate can be used in a number of applications, such as nonlocal quantum interference experiments, the generation of entangled Schrodinger cat states 4 , and in fusion operations for generating cluster states 11 . More generally, a quantum encoder gate 10 could be used in combination with a destructive controlled-phase gate to preserve the value of the control qubit, but that would require an additional ancilla photon.…”

“…There are potential applications where it would be desirable to produce a controlled phase shift on a state containing a larger number of photons, such as a coherent state. This can be useful in producing Schrodinger cat states 2 or in quantum interference experiments, for example 3,4 .…”

“…This is a very useful operation since it is a universal gate for quantum computation when combined with single-qubit operations 1 . It can also be used to create Schrodinger cat states 2 , to perform nonlocal quantum interferometry with violations of Bell's inequality 3,4 , and to implement complete Bell state measurements in quantum teleportation 5,6 , for example.…”

“…The same devices can be used to implement fusion gates that allow the construction of a cluster state 11 . As another example, Bell's inequality can be violated in nonlocal interferometer experiments in which a controlled-phase shift is combined with homodyne measurements 4 . The control qubit is destroyed in a postselection process in experiments of that kind, which allows the use of the controlled-phase gate described here.…”